While you are new, concentrate on playing only 1v1 against 2v2. 2v2 is more complex and requires good teamwork and communication. With limited game slots (of 5 games), it can get quite boring or even annoying to wait as long as 2 weeks to cycle through all 4 players.
If you like the game, then purchase anything to bump the game limit up to 20. A specific purchase, the Game Limit Upgrade found at the in-app Store, can bump it up to 35 games!
(Almost always,) boost your specials and snipers.
Boost your soldiers. It gives your opponent less options and makes him/her spend more wits to kill your boosted soldier.
Kill the unit you attacked on the same turn. Leaving an enemy unit with even 1 hp left can be healed by an enemy medic and/or deal damage on your units during the next turn.
Guard the backdoor. You avoid losing through a rush.
When rushed, snipers can be a lifesaver. Point-blank, they deal 3 damage the cheapest possible way.
If you want to be really good at this game, you should be like a sponge. Absorb as much as you can from the forums, specifically this thread and the Super-Titan replay thread. I highly suggest being active at the forums. People here are really very helpful and nice.
Don't be afraid to lose. We all learn (the most) from our mistakes (losses).
Copy all your replays/link to a text editor. Post them on the Share Your Replays thread. Ask for suggestions on how you could have played better. :)[hr]
Keep your important units out of the reach of the enemy units if you can not really afford losing them. Retreating a unit one or two hexes can buy you time to reinforce or shield them with other expendable units.